Method and apparatus for digital predistortion for a switched mode power amplifier

ABSTRACT

A method includes receiving an input signal and predistorting a baseband representation of the input signal at a carrier frequency and at one or more harmonic frequencies. The method also includes generating an output signal based on the predistorted baseband representation of the input signal, and transmitting the output signal to a power amplifier. Predistorting the baseband representation of the input signal at the carrier frequency could occur in parallel with predistorting the baseband representation of the input signal at the one or more harmonic frequencies.

TECHNICAL FIELD

This disclosure is generally directed to power amplification. Morespecifically, this disclosure is directed to a method and apparatus fordigital predistortion for a switched mode power amplifier, such as foruse in a wireless transmitter.

BACKGROUND

Power amplifiers (PAs) are inherently nonlinear devices that are used ina wide variety of communication systems. Digital baseband predistortionis a highly cost-effective way to linearize a power amplifier.Unfortunately, most existing predistortion architectures assume that apower amplifier has a “memoryless” nonlinearity. This means that thesearchitectures assume the output current of a power amplifier dependsonly on the input current of the power amplifier.

SUMMARY

This disclosure provides an apparatus and method for digitalpredistortion for a switched mode power amplifier.

In a first example, a method includes receiving an input signal andpredistorting a baseband representation of the input signal at a carrierfrequency and at one or more harmonic frequencies. The method alsoincludes generating an output signal based on the predistorted basebandrepresentation of the input signal, and transmitting the output signalto a power amplifier.

In a second example, an apparatus includes a digital predistortion blockhaving a first processing unit and second processing units. The firstprocessing unit is configured to receive an input signal and predistorta baseband representation of the input signal at a carrier frequency.The second processing units are configured to receive the input signaland predistort a baseband representation of the input signal at one ormore harmonic frequencies. The digital predistortion block configured togenerate an output signal based on the predistorted basebandrepresentation of the input signal and transmit the output signal to apower amplifier.

In a third example, a non-transitory computer readable medium is encodedwith computer-executable instructions. The instructions when executedcause at least one processing device to receive an input signal,predistort a baseband representation of the input signal at a carrierfrequency and at one or more harmonic frequencies, generate an outputsignal based on the predistorted baseband representation of the inputsignal, and transmit the output signal to a power amplifier.

Other technical features may be readily apparent to one skilled in theart from the following figures, descriptions, and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of this disclosure and its features,reference is now made to the following description, taken in conjunctionwith the accompanying drawings, in which:

FIG. 1 illustrates a problem of nonlinearity in power amplifiers such asswitched mode power amplifiers;

FIGS. 2A and 2B illustrate some causes and effects of nonlinearity inpower amplifiers;

FIG. 3 illustrates an example signal response of a nonlinear poweramplifier;

FIG. 4 illustrates an example digital predistortion (DPD) system for usewith a power amplifier according to this disclosure;

FIG. 5 illustrates an example implementation of a DPD processing blockfor use within a DPD system according to this disclosure;

FIG. 6 illustrates an example signal response of a switched mode poweramplifier according to this disclosure;

FIG. 7 illustrates an example implementation of a DPD processing blockfor use within a DPD system that supports distortions caused by aswitched mode power amplifier according to this disclosure;

FIGS. 8 and 9 illustrate example test results showing an improvement ofnonlinearity using a DPD system according to this disclosure; and

FIG. 10 illustrates an example method for digital predistortionaccording to this disclosure.

DETAILED DESCRIPTION

FIGS. 1 through 10, discussed below, and the various examples used todescribe the principles of the present invention in this patent documentare by way of illustration only and should not be construed in any wayto limit the scope of the invention. Those skilled in the art willunderstand that the principles of the present invention may beimplemented in any suitable manner and in any type of suitably arrangeddevice or system.

Power amplifiers (PAs) are ubiquitous components in communicationsystems, particularly in wireless transmitters. Most PAs are inherentlynonlinear, meaning their outputs are not linearly related to theirinputs. It is well-known that there is an approximately inverserelationship between the efficiency and linearity of a PA. Hence,nonlinear PAs are desirable from an efficiency point of view. However,the nonlinearity may cause spectral regrowth (broadening), which leadsto adjacent channel interference. Nonlinearity may also cause in-banddistortion, which degrades the bit error rate (BER) performance. Sometransmission formats are particularly vulnerable to PA nonlinearitiesdue to their high peak-to-average power ratios, which correspond tolarge fluctuations in their signal envelopes. In order to comply withspectral masks imposed by regulatory bodies and to reduce BER, PAlinearization may be necessary.

Of all PA linearization techniques, digital baseband predistortion isamong the most cost-effective. A predistorter is a functional block thatprecedes the PA. The predistorter generally acts to create an expandingnonlinearity in the PA input signal since the PA has a compressingcharacteristic. In an ideal case, the PA output would be a scalarmultiple of the input to the predistorter-PA chain. For a memoryless PA(meaning a PA whose output current depends only on its input current),memoryless predistortion is sufficient.

Like many other power amplifiers, switched mode PAs exhibit nonlinearbehaviors, but the nonlinearity of switched mode PAs is typically worsefor higher output powers and higher efficiency operations. Fordiscrete-time switching signals driving a switched mode PA, thenonlinearity comes from a non-ideal switching waveform, such asrise/fall time mismatches. Typical digital predistortion techniques maynot be able to linearize this type of amplifier.

Embodiments of this disclosure provide predistorter models that capturenonlinearity behaviors of switching signals for a switched mode PA. Thepredistorter models disclosed here include terms that are not present inpredistorter models for other types of PAs. Among other things, thedisclosed embodiments help a switched mode PA to meet linearityrequirements defined by industry standards. Without the disclosedpredistorter models, the PA may have to back off significantly, whichreduces output power and efficiency.

The embodiments disclosed here are applicable to various communicationsystems, such as those where efficiency and cost considerations of apower amplifier system are important factors. For example, the disclosedembodiments can be applicable for use in a wireless transmitter (such asa portable device or a base station) in a number of wireless mobilecommunication systems (such as LTE, LTE-A, or 5G). It will be understoodthat the disclosed embodiments may be applicable in other communicationsystems, as well.

FIG. 1 illustrates a problem of nonlinearity in power amplifiers such asswitched mode PAs. In FIG. 1, an amplitude response of a nonlinear PA isplotted over a range of frequencies. As indicated at reference numerals100-102, the nonlinearity of the PA leads to a high adjacent channelpower ratio (ACPR), which is undesirable in most systems.

FIGS. 2A and 2B illustrate some causes and effects of nonlinearity inpower amplifiers. In FIG. 2A, a plot 201 depicts a square waveform foran ideal power amplifier. As shown in FIG. 2A, the plot 201 exhibitsstraight vertical and horizontal lines without distortion. In contrast,in FIG. 2B, a plot 203 depicts a representative example waveform of apower amplifier, such as a switched mode PA. The plot 203 shows a numberof distortions that cause PA inefficiencies and that lead to excesspower usage. For example, distortions 205 in the vertical lines of thewaveform can be caused by rise and fall time mismatches in the PA.Likewise, distortions 207 in the horizontal lines of the waveform can becaused by a finite resistance of a transistor in the switching state.

FIG. 3 illustrates an example signal response of a nonlinear PA 300. InFIG. 3, the PA 300 receives an input signal 301 that is concentrated ata carrier frequency Fc. The narrow bandwidth of the input signal 301indicates minimal signal spreading. The input signal 301 also includeslittle or no components at harmonic frequencies, such as 2Fc and 3Fc.

As shown in FIG. 3, signal spreading in an output signal 303 occurs atthe carrier frequency Fc and at the harmonic frequencies (such as 2Fcand 3Fc) due to the PA 300. In some transmitter implementations, onlynonlinearity around the carrier frequency Fc is important, and thenonlinear signals around the harmonic frequencies can be greatlyattenuated by an output-matching network 302 of the PA. As a result, inmany implementations, it is only important to linearize the carrierfrequency Fc, and the harmonic frequencies (such as 2Fc and 3Fc) can belargely ignored.

The linearization of a PA signal is largely determined by the digitalpredistortion (DPD) model that is used. If a non-optimal DPD model isselected for use with a given nonlinear PA, the linearization resultswill also be less than optimal.

Note that the PA 300 here may be part of a larger system, such as atransmitter, that includes other components. Also note that the inputsignal 301 and the output signal 303 may include other signal componentsat other frequencies.

FIG. 4 illustrates an example digital predistortion (DPD) system 400 foruse with a power amplifier according to this disclosure. As shown inFIG. 4, the DPD system 400 includes a DPD block 405, a digital-to-analogconverter (DAC) 410, an up-converter 415, a power amplifier 420, asignal coupler 425, a down-converter 430, an analog-to-digital converter(ADC) 435, and a training algorithm block 440. The power amplifier 420could be coupled to an output-matching network, such as is shown in FIG.3.

The DPD block 405 acts to reverse or cancel signal compressingcharacteristics of the PA 420 through spectrum widening of an inputsignal. The spectrum widening generated by the DPD block 405 ispreserved as the signal passes through the DAC 410 and the up-converter415. Thus, when the signal passes through the DPD block 405 and the PA420, the result is a much more linear response.

In the DPD system 400, the DPD block 405 is trained as a nonlinearpre-inverse of the PA 420, which creates a spectral widening signal(spectral regrowth) at the output of the DPD block 405. The output ispreserved in the analog chain through the DAC 410 and the up-converter415 before reaching the PA 420 in order to substantially cancel out thePA nonlinearity. The up-converter 415 can upconvert the output of theDAC 410 to a higher frequency signal, such as a radio frequency (RF)signal.

In the DPD system 400 (as in many digital predistortion systems), thenonlinear behavior of the PA 420 may not be known beforehand. Thus, afeedback path with a bandwidth similar to the DPD bandwidth is used totrain the DPD block 405. The feedback path here includes the coupler425, the down-converter 430, the ADC 435, and the training algorithmblock 440. The coupler 425 receives a portion of the output signal fromthe PA 420 and sends the output signal to the down-converter 430, whichprovides a lower-frequency signal to the ADC 435. The output from theADC 435 and the input to the DPD block 405 are received at the trainingalgorithm block 440, which includes one or more training algorithms. Thetraining algorithm block 440 can use stored parameters and trainingalgorithms to determine the best DPD model for the DPD block 405 inorder to cancel the nonlinearity of the PA 420.

In some systems, difficulties arise because the PA 420 is a nonlinearsystem with memory, which means the output current of the PA 420 is notdependent only on the input current of the PA 420. As a result, it canbe difficult to model and construct an inverse function to be used fordigital predistortion.

Baseband and Passband Relationships

Physical systems process real signals. In communication systems,baseband signals are typically in complex form to represent both signalsmodulated to RF carriers with a quadrature phase relationship. Assumethe terms {tilde over (x)}(t) and {tilde over (y)}(t) are used to denotebaseband input and output signals, respectively. Also assume the termsx(t) and y(t) are used to denote passband input and output signals,respectively. Their relationships can be given as:x(t)=Re[{tilde over (x)}(t)e ^(jω) ⁰ ^(t)]  (1){tilde over (x)}(t)=2LPF[x(t)e ^(−jω) ⁰ ^(t)]  (2)y(t)=Re[{tilde over (y)}(t)e ^(jω) ⁰ ^(t)]  (3){tilde over (y)}(t)=2LPF[y(t)e ^(−jω) ⁰ ^(t)]  (4)where ω₀ is the carrier frequency and LPF stands for a low-pass filter.The term x(t) can also be written as:x(t)=½[{tilde over (x)}(t)e ^(jω) ⁰ ^(t) +{tilde over (x)}*(t)e ^(−jω) ⁰^(t)]  (5)

For a real input signal, x(t), the Volterra Series can be used torepresent a nonlinear system as

$\begin{matrix}{{y(t)} = {\sum\limits_{k}{\int\mspace{14mu}{\ldots\mspace{14mu}{\int{{h_{k}( \tau_{k} )}{\prod\limits_{i = 1}^{k}{{x( {t - \tau_{i}} )}{\mathbb{d}\tau_{k}}}}}}}}}} & (6)\end{matrix}$where τ_(k)=[τ₁, . . . , τ_(k)]^(T), h_(k)(.) is the k-th order Volterrakernel, and dτ_(k)=dτ₁ dτ₂ . . . dτ_(k).

Substituting Equation (5) into Equation (6), it can been seen that thereare terms located around e^(±jω) ⁰ ^(t), which are related to the signalin the fundamental frequency zone. In some implementations, there arealso terms located at e^(±jnω) ⁰ ^(t), which are related to signals inthe harmonic frequency zones. In many implementations, only the signalin the fundamental zone is important since the signals in the harmonicfrequency zones do not interact with the signal at the fundamentalfrequency and can be ignored or filtered out by analog filters. If allof the terms located around e^(±jω) ⁰ ^(t) are collected aftersubstituting Equation (5) into Equation (6), it can be shown that:

$\begin{matrix}{{y(t)} = {{{\mathbb{e}}^{{- j}\;\omega_{o}t}{\sum\limits_{k}{\int\mspace{14mu}{\ldots\mspace{14mu}{\int{\frac{\begin{pmatrix}{{2k} + 1} \\k\end{pmatrix}}{2^{{2k} + 1}}{h_{{2k} + 1}( \tau_{{2k} + 1} )}{\prod\limits_{i = 1}^{k}{{\overset{\sim}{x}( {t - \tau_{i}} )}{\mathbb{e}}^{{- j}\;\omega_{o}\tau_{i}}{\prod\limits_{i = {k + 1}}^{{2k} + 1}{{{\overset{\sim}{x}}^{*}( {t - \tau_{i}} )}{\mathbb{e}}^{j\;\omega_{o}\tau_{i}}{\mathbb{d}\tau_{{2k} + 1}}}}}}}}}}}} + {{\mathbb{e}}^{j\;\omega_{o}t}{\sum\limits_{k}{\int\mspace{14mu}{\ldots\mspace{14mu}{\int{\frac{\begin{pmatrix}{{2k} + 1} \\k\end{pmatrix}}{2^{{2k} + 1}}{h_{{2k} + 1}( \tau_{{2k} + 1} )}{\prod\limits_{i = 1}^{k + 1}{{\overset{\sim}{x}( {t - \tau_{i}} )}{\mathbb{e}}^{{- j}\;\omega_{o}\tau_{i}}{\prod\limits_{i = {k + 2}}^{{2k} + 1}{{{\overset{\sim}{x}}^{*}( {t - \tau_{i}} )}{\mathbb{e}}^{j\;\omega_{o}\tau_{i}}{\mathbb{d}\tau_{{2k} + 1}}}}}}}}}}}}}} & (7)\end{matrix}$

Substituting Equation (7) into Equation (4), it can be seen that thebaseband representation is:

$\begin{matrix}{{\overset{\sim}{y}(t)} = {\sum\limits_{k}{\int\mspace{14mu}{\ldots\mspace{14mu}{\int{{{\overset{\sim}{h}}_{{2k} + 1}( \tau_{{2k} + 1} )}{\prod\limits_{i = 1}^{k + 1}{{\overset{\sim}{x}( {t - \tau_{i}} )}{\prod\limits_{i = {k + 2}}^{{2k} + 1}{{{\overset{\sim}{x}}^{*}( {t - \tau_{i}} )}{\mathbb{d}\tau_{{2k} + 1}}}}}}}}}}}} & (8)\end{matrix}$where

$\begin{matrix}{{{\overset{\sim}{h}}_{{2k} + 1}( \tau_{{2k} + 1} )} = {\frac{1}{2^{2k}}\begin{pmatrix}{{2k} + 1} \\k\end{pmatrix}{h_{{2k} + 1}( \tau_{{2k} + 1} )}{\prod\limits_{i = 1}^{k + 1}{{\mathbb{e}}^{{- j}\;\omega_{o}\tau_{i}}{\prod\limits_{i = {k + 2}}^{{2k} + 1}{\mathbb{e}}^{j\;\omega_{o}\tau_{i}}}}}}} & (9)\end{matrix}$

In the discrete-time domain, Equation (8) becomes:

$\begin{matrix}{{\overset{\sim}{y}(n)} = {\sum\limits_{k}{\sum\limits_{l_{1}}\mspace{14mu}{\ldots\mspace{14mu}{\sum\limits_{l_{{2k} + 1}}{{{\overset{\sim}{h}}_{{2k} + 1}( {l_{1},l_{2},\ldots\mspace{14mu},l_{{2k} + 1}} )}{\prod\limits_{i = 1}^{k + 1}{{\overset{\sim}{x}( {n - l_{i}} )}{\prod\limits_{i = {k + 2}}^{{2k} + 1}{{\overset{\sim}{x}}^{*}( {n - l_{i}} )}}}}}}}}}} & (10)\end{matrix}$where l₁, l₂, . . . , l_(2k+1) are delay terms.

The model represented in Equation (10) is the most generalrepresentation. However, this model may be difficult to implement sincethe number of terms in the model increases dramatically as the nonlinearorder and memory depth increase. Practical models often simplify themodel to reduce complexity while maintaining good modeling accuracy.

Memoryless PA and PA with Memory Effects

A memoryless passband PA model can be derived by setting all the delayterms, l_(i), in Equation (10) to zero, which leads to:

$\begin{matrix}{{\overset{\sim}{y}(n)} = {\sum\limits_{k}{{{\overset{\sim}{h}}_{{2k} + 1}( {0,0,\ldots\mspace{14mu},0} )}{\prod\limits_{i = 1}^{k + 1}{{\overset{\sim}{x}(n)}{\prod\limits_{i = {k + 2}}^{{2k} + 1}{{\overset{\sim}{x}}^{*}(n)}}}}}}} & (11)\end{matrix}$

$\begin{matrix}{{\overset{\sim}{y}(n)} = {\sum\limits_{k}{{\overset{\sim}{h}}_{{2k} + 1}{{\overset{\sim}{x}}^{k + 1}(n)}{{\overset{\sim}{x}}^{*k}(n)}}}} & (12)\end{matrix}$

A passband PA with memory effects can be modeled by setting all delayterms, l_(i), in Equation (10) to the same value, which leads to:

$\begin{matrix}{{\overset{\sim}{y}(n)} = {\sum\limits_{k}{\sum\limits_{l}{{{\overset{\sim}{h}}_{{2k} + 1}( {l,l,\ldots\mspace{14mu},l} )}{\prod\limits_{i = 1}^{k + 1}{{\overset{\sim}{x}( {n - l} )}{\prod\limits_{i = {k + 2}}^{{2k} + 1}{{\overset{\sim}{x}}^{*}( {n - l} )}}}}}}}} & (13)\end{matrix}$

$\begin{matrix}{{\overset{\sim}{y}(n)} = {\sum\limits_{k}{\sum\limits_{l}{{{\overset{\sim}{h}}_{{2k} + 1}(l)}{{\overset{\sim}{x}}^{k + 1}( {n - l} )}{{\overset{\sim}{x}}^{*k}( {n - l} )}}}}} & (14)\end{matrix}$

There are other ways to simplify the model. Regardless of thesimplification used, the model includes one more x(n−l_(i)) term thanthe x*(n−l_(i)) term, as shown in Equation (10).

In order to correct the nonlinearity of a memoryless PA or a PA withmemory effects, a DPD (such as the DPD 405 shown in FIG. 4) can beimplemented before the PA in the transmission stream. The DPD can bemodeled mathematically based on the equations shown above. For example,a memoryless DPD can be used to predistort the memoryless PA model shownin Equation (12). Similarly, a memory DPD can be used to predistort thePA model with memory effects shown in Equation (14).

In the physical implementation of a DPD, some of the calculations can bemodeled using lookup tables (LUTs). For example, starting with Equation(12) (which is repeated below), a memoryless DPD model using LUTs can bederived as follows:

$\begin{matrix}{{\overset{\sim}{y}(n)} = {\sum\limits_{k}{{\overset{\sim}{h}}_{{2k} + 1}{{\overset{\sim}{x}}^{k + 1}(n)}{{\overset{\sim}{x}}^{*k}(n)}}}} & (12)\end{matrix}$

$\begin{matrix}{{\overset{\sim}{y}(n)} = {\sum\limits_{k}{{\overset{\sim}{h}}_{{2k} + 1}{\overset{\sim}{x}(n)}{{\overset{\sim}{x}(n)}}^{2k}}}} & (15)\end{matrix}$

$\begin{matrix}{{\overset{\sim}{y}(n)} = {{\overset{\sim}{x}(n)}{\sum\limits_{k}{{\overset{\sim}{h}}_{{2k} + 1}{{\overset{\sim}{x}(n)}}^{2k}}}}} & (16)\end{matrix}${tilde over (y)}(n)={tilde over (x)}(n)LUT[|{tilde over (x)}(n)|²]  (17)

Accordingly, Equation (17) can be executed by one or more processingblocks within the memoryless DPD.

For a memory DPD, a model using LUTs can be derived as follows, startingwith Equation (14) (which is repeated below):

$\begin{matrix}{{\overset{\sim}{y}(n)} = {\sum\limits_{k}{\sum\limits_{l}{{{\overset{\sim}{h}}_{{2k} + 1}(l)}{{\overset{\sim}{x}}^{k + 1}( {n - l} )}{{\overset{\sim}{x}}^{*k}( {n - l} )}}}}} & (14)\end{matrix}$

$\begin{matrix}{{\overset{\sim}{y}(n)} = {\sum\limits_{k}{\sum\limits_{l}{{{\overset{\sim}{h}}_{{2k} + 1}(l)}{\overset{\sim}{x}( {n - l} )}{{\overset{\sim}{x}( {n - l} )}}^{2k}}}}} & (18)\end{matrix}$

$\begin{matrix}{{\overset{\sim}{y}(n)} = {\sum\limits_{l}{{\overset{\sim}{x}( {n - l} )}{\sum\limits_{k}{{{\overset{\sim}{h}}_{{2k} + 1}(l)}{{\overset{\sim}{x}( {n - l} )}}^{2k}}}}}} & (19)\end{matrix}$

$\begin{matrix}{{\overset{\sim}{y}(n)} = {\sum\limits_{l}{{\overset{\sim}{x}( {n - l} )}{{LUT}_{l}\lbrack {{\overset{\sim}{x}( {n - l} )}}^{2} \rbrack}}}} & (20)\end{matrix}$

Accordingly, Equation (20) can be executed by one or more processingblocks within the memory DPD.

FIG. 5 illustrates an example implementation of a DPD processing block500 for use within a DPD system according to this disclosure. In someembodiments, the DPD processing block 500 may represent or be used inconnection with the DPD block 405 of FIG. 4. In particular embodiments,the DPD processing block 500 implements the PA model with memory effectsdescribed above.

As shown in FIG. 5, the DPD processing block 500 includes a plurality oflookup tables (LUTs) 501 a-501 c, a plurality of delay elements 503, anabsolute value squaring operator 505, a plurality of multipliers 507,and an adder 509. The number of LUTs and delay elements can bedetermined by the memory order of the DPD processing block 500. In FIG.5, the memory order is three, so there are three LUTs in the DPDprocessing block 500.

The DPD processing block 500 receives a DPD input signal {tilde over(x)}(n) and processes the DPD input signal using the LUTs 501 a-501 cand the mathematical operators according to Equation (20) above(implemented using the multipliers 507 and the adder 509). The DPDprocessing block 500 generates the pre-inversed DPD output signal {tildeover (y)}(n), which is transmitted to the memoryless PA where the signalis linearized such as shown in FIG. 4.

Although FIG. 5 shows three LUTs 501 a-501 c, it will be understood thatmore or fewer LUTs and delay elements may be used as required based onthe memory order. For example, in higher-order models, the memory ordermay be equal to four, five, six, or another value. In suchimplementations, the number of LUTs and delay elements may be adjustedaccordingly.

Digital baseband predistortion is a highly cost-effective way tolinearize PAs, but many architectures assume that the PA has amemoryless nonlinearity. However, for some types of power amplifiers(such as a switched mode PAs), PA memory effects cannot be ignored, andmemoryless DPD has limited effectiveness.

FIG. 6 illustrates an example signal response of a switched mode PAaccording to this disclosure. As shown in FIG. 6, the PA 600 receives aninput signal 601 and processes the signal to generate an output signal603. The PA 600 is a switched mode PA, which operates like a switch andtherefore exhibits different nonlinearity characteristics than othertypes of PAs. In many respects, the switching properties of the switchedmode PA 600 are more characteristic of a digital PA than an analog PA.Likewise, the signal going through the PA 600 exhibits digital-likesignal properties with aliasing content. For example, as shown in FIG.6, the input signal 601 to the PA 600 resembles a digital signal, withhigher amplitudes at the carrier frequency Fc and at harmonicfrequencies 2Fc and 3Fc. This is in contrast to the PA input signal 301shown in FIG. 3, which is concentrated at the carrier frequency Fc withlittle or no amplitude at the harmonic frequencies 2Fc and 3Fc.

The aliasing and nonlinearity of the switched mode PA 600 can causeharmonic contents to fold back in-band. That is, when nonlineardistortion occurs, the nonlinear signal in each harmonic zone can foldback into the fundamental zone because of aliasing. For example, in FIG.6, nonlinear versions of the input signal 601 at harmonic frequencies2Fc and 3Fc may fold into the output signal 603 at the carrier frequencyFc.

As a result, the output signal 603 at the carrier frequency Fc canexhibit significant nonlinearity. Some of these distortions at thecarrier frequency Fc are a result of the input signal 601 at theharmonic frequencies 2Fc and 3Fc. Similar nonlinearities occur at theoutput signal 603 at the harmonic frequencies 2Fc and 3Fc. Thus, asshown in FIG. 6, the output signal 603 exhibits significant spectrumwidening at the carrier frequency Fc and at the harmonic frequencies 2Fcand 3Fc. Many DPDs may not be able to handle these distortions caused byharmonic folding.

Note that the PA 600 may be part of a larger system, such as a wirelesstransmitter, that includes other components. Also note that the inputsignal 601 and the output signal 603 may include components at harmonicfrequencies higher than 3Fc (such as 4Fc, 5Fc, and so on).

Because of the distortions caused by harmonic folding, it is helpful toprovide a baseband representation of signals in higher order harmoniczones. These signals (or nonlinear distortions) are located at harmonicfrequencies. The digital nature of the signal causes the distortions tofold back to the fundamental frequency through aliasing.

To model this, the signal components located at the m-th harmonic zoneare derived, based on Equation (7). If the terms around the m-thharmonic zone are selected, some of the 1's in Equation (7) are replacedwith m's, and Equation (7) becomes the following:

$\begin{matrix}{{y(t)} = {{{\mathbb{e}}^{{- j}\; m\;\omega_{o}t}{\sum\limits_{k}{\int\mspace{14mu}{\ldots\mspace{14mu}{\int\ {\frac{\begin{pmatrix}{{2\; k} + m} \\k\end{pmatrix}}{2^{{2\; k} + m}}{h_{{2\; k} + m}( \tau_{{2\; k} + m} )}{\prod\limits_{i = 1}^{k}\;{{\overset{\sim}{x}( {t - \tau_{i}} )}{\mathbb{e}}^{{- j}\;\omega_{o}\tau_{i}}{\prod\limits_{i = {k + 1}}^{{2\; k} + m}\;{{{\overset{\sim}{x}}^{*}( {t - \tau_{i}} )}{\mathbb{e}}^{{j\omega}_{o}\tau_{i}}{\mathbb{d}\tau_{{2\; k} + m}}}}}}}}}}}} + {{\mathbb{e}}^{j\; m\;\omega_{o}t}{\sum\limits_{k}{\int\mspace{14mu}{\ldots\mspace{14mu}{\int{\frac{\begin{pmatrix}{{2\; k} + m} \\k\end{pmatrix}}{2^{{2\; k} + m}}{h_{{2\; k} + m}( \tau_{{2\; k} + m} )}{\prod\limits_{i = 1}^{k + m}\;{{\overset{\sim}{x}( {t - \tau_{i}} )}{\mathbb{e}}^{{- j}\;\omega_{o}\tau_{i}}{\prod\limits_{i = {k + m + 1}}^{{2\; k} + m}\;{{{\overset{\sim}{x}}^{*}( {t - \tau_{i}} )}{\mathbb{e}}^{j\;\omega_{o}\tau_{i}}{\mathbb{d}\tau_{{2\; k} + m}}}}}}}}}}}}}} & (21)\end{matrix}$

Aliasing with e^(j(m+1)ω) ⁰ ^(t) causes the first term on the right handside of Equation (21) to be aliased back to the fundamental frequency.The baseband representation can be written as:

$\begin{matrix}{{{\overset{\sim}{y}}_{mc}(t)} = {\sum\limits_{k}{\int\mspace{14mu}{\ldots\mspace{14mu}{\int{{{\overset{\sim}{h}}_{{{2\; k} + m},{mc}}( \tau_{{2\; k} + m} )}{\prod\limits_{i = 1}^{k}\;{{\overset{\sim}{x}( {t - \tau_{i}} )}{\prod\limits_{i = {k + 1}}^{{2\; k} + m}\;{{{\overset{\sim}{x}}^{*}( {t - \tau_{i}} )}{\mathbb{d}\tau_{{2\; k} + m}}}}}}}}}}}} & (22)\end{matrix}$where

$\begin{matrix}{{{\overset{\sim}{h}}_{{{2\; k} + m},{mc}}( \tau_{{2\; k} + m} )} = {\frac{1}{2^{{2\; k} + m - 1}}\begin{pmatrix}{{2\; k} + m} \\k\end{pmatrix}{h_{{2\; k} + m}( \tau_{{2\; k} + m} )}{\prod\limits_{i = 1}^{k}\;{{\mathbb{e}}^{{- j}\;\omega_{o}\tau_{i}}{\prod\limits_{i = {k + 1}}^{{2\; k} + m}\;{\mathbb{e}}^{j\;\omega_{o}\tau_{i}}}}}}} & (23)\end{matrix}$

The discrete-time model is given by:

$\begin{matrix}{{{\overset{\sim}{y}}_{mc}(n)} = {\sum\limits_{k}\;{\sum\limits_{l_{1}}\mspace{20mu}{\ldots\mspace{14mu}{\sum\limits_{l_{{2\; k} + 1}}\;{{{\overset{\sim}{h}}_{{{2\; k} + m},{mc}}( {l_{1},l_{2},\ldots\mspace{14mu},l_{{2k} + m}} )}{\prod\limits_{i = 1}^{k}\;{{\overset{\sim}{x}( {n - l_{i}} )}{\prod\limits_{i = {k + 1}}^{{2\; k} + m}\;{{\overset{\sim}{x}}^{*}( {n - l_{i}} )}}}}}}}}}} & (24)\end{matrix}$

Here, m can be 0, 1, 2, 3, . . . . For any m that is a non-negativeinteger, the resulting terms are not present in the model shown inEquation (10). If all delay terms, l_(i), are set to be equal, then themodel is simplified to:

$\begin{matrix}{{{\overset{\sim}{y}}_{mc}(n)} = {\sum\limits_{k}{\sum\limits_{l}{{{\overset{\sim}{h}}_{{{2\; k} + m},{mc}}(l)}{\prod\limits_{i = 1}^{k}\;{{\overset{\sim}{x}( {n - l} )}{\prod\limits_{i = {k + 1}}^{{2\; k} + m}\;{{\overset{\sim}{x}}^{*}( {n - l} )}}}}}}}} & (25) \\{\mspace{70mu}{= {\sum\limits_{k}{\sum\limits_{l}{{{\overset{\sim}{h}}_{{{2\; k} + m},{mc}}(l)}{{\overset{\sim}{x}}^{*m}( {n - l} )}{{\overset{\sim}{x}( {n - l} )}}^{2\; k}}}}}} & (26) \\{\mspace{70mu}{= {\sum\limits_{l}{{{\overset{\sim}{x}}^{*m}( {n - l} )}{\sum\limits_{k}{{{\overset{\sim}{h}}_{{{2\; k} + m},{mc}}(l)}{{\overset{\sim}{x}( {n - l} )}}^{2\; k}}}}}}} & (27) \\{\mspace{70mu}{= {\sum\limits_{l}{{{\overset{\sim}{x}}^{*m}( {n - l} )}{{LUT}_{l,{mc}}\lbrack {{\overset{\sim}{x}( {n - l} )}}^{2\;} \rbrack}}}}} & (28)\end{matrix}$

Aliasing with e^(−(m−1)ω) ⁰ ^(t) causes the second term on the righthand side of Equation (21) to be aliased back to the fundamentalfrequency. The baseband representation can be written as:

$\begin{matrix}{{{\overset{\sim}{y}}_{m}(t)} = {\sum\limits_{k}{\int\mspace{14mu}{\ldots\mspace{14mu}{\int{{{\overset{\sim}{h}}_{{{2\; k} + m},m}( \tau_{{2\; k} + m} )}{\prod\limits_{i = 1}^{k + m}\;{{\overset{\sim}{x}( {t - \tau_{i}} )}{\prod\limits_{i = {k + m + 1}}^{{2\; k} + m}\;{{{\overset{\sim}{x}}^{*}( {t - \tau_{i}} )}{\mathbb{d}\tau_{{2\; k} + m}}}}}}}}}}}} & (29)\end{matrix}$where

$\begin{matrix}{{{\overset{\sim}{h}}_{{{2\; k} + m},m}( \tau_{{2\; k} + m} )} = {\frac{1}{2^{{2\; k} + m - 1}}\begin{pmatrix}{{2\; k} + m} \\k\end{pmatrix}{h_{{2\; k} + m}( \tau_{{2\; k} + m} )}{\prod\limits_{i = 1}^{k + m}\;{{\mathbb{e}}^{{- j}\;\omega_{o}\tau_{i}}{\prod\limits_{i = {k + m + 1}}^{{2\; k} + m}\;{\mathbb{e}}^{j\;\omega_{o}\tau_{i}}}}}}} & (30)\end{matrix}$

The discrete-time model is given by:

$\begin{matrix}{{{\overset{\sim}{y}}_{m}(n)} = {\sum\limits_{k}\;{\sum\limits_{l_{1}}\mspace{20mu}{\ldots\mspace{14mu}{\sum\limits_{l_{{2\; k} + 1}}\;{{{\overset{\sim}{h}}_{{{2\; k} + m},m}( {l_{1},l_{2},\ldots\mspace{14mu},l_{{2k} + m}} )}{\prod\limits_{i = 1}^{k + m}\;{{\overset{\sim}{x}( {n - l_{i}} )}{\prod\limits_{i = {k + m + 1}}^{{2\; k} + m}\;{{\overset{\sim}{x}}^{*}( {n - l_{i}} )}}}}}}}}}} & (31)\end{matrix}$

Here, m can be 0, 2, 3, . . . . When m=1, the model becomes Equation(10). For any other m that is a non-negative integer, the resultingterms are not present in the model shown in Equation (10). If all delayterms, l_(i), are set to be equal, then the model is simplified to:

$\begin{matrix}{{{\overset{\sim}{y}}_{m}(n)} = {\sum\limits_{k}{\sum\limits_{l}{{{\overset{\sim}{h}}_{{{2\; k} + m},m}(l)}{\prod\limits_{i = 1}^{k + m}\;{{\overset{\sim}{x}( {n - l} )}{\prod\limits_{i = {k + m + 1}}^{{2\; k} + m}\;{{\overset{\sim}{x}}^{*}( {n - l} )}}}}}}}} & (32) \\{\mspace{59mu}{= {\sum\limits_{k}{\sum\limits_{l}{{{\overset{\sim}{h}}_{{{2\; k} + m},m}(l)}{{\overset{\sim}{x}}^{m}( {n - l} )}{{\overset{\sim}{x}( {n - l} )}}^{2\; k}}}}}} & (33) \\{\mspace{59mu}{= {\sum\limits_{l}{{{\overset{\sim}{x}}^{m}( {n - l} )}{\sum\limits_{k}{{{\overset{\sim}{h}}_{{{2\; k} + m},m}(l)}{{\overset{\sim}{x}( {n - l} )}}^{2\; k}}}}}}} & (34) \\{\mspace{59mu}{= {\sum\limits_{l}{{{\overset{\sim}{x}}^{m}( {n - l} )}{{LUT}_{l,m}\lbrack {{\overset{\sim}{x}( {n - l} )}}^{2\;} \rbrack}}}}} & (35)\end{matrix}$

FIG. 7 illustrates an example implementation of a DPD processing block700 for use within a DPD system that supports distortions caused by aswitched mode PA according to this disclosure. In some embodiments, theDPD processing block 700 may represent or be used in connection with theDPD block 405 of FIG. 4. It will be understood that the DPD processingblock 700 may be used with other systems, as well.

As shown in FIG. 7, the DPD processing block 700 includes three DPDprocessing units 710, 720, 730. Like the DPD processing block 500 ofFIG. 5, each DPD processing unit 710-730 include a plurality of LUTs,delay elements, an absolute value squaring operator, a plurality ofmultipliers, and an adder. In addition, the DPD processing unit 720includes an exponent operator 725, and the DPD processing unit 730includes a conjugate exponent operator 735. The number of LUTs and delayelements in each processing unit 710-730 can be determined by the memoryorder of the DPD processing block 700. In FIG. 7, the memory order is 3,so there are three LUTs in each DPD processing unit 710-730.

The DPD processing block 700 receives the DPD input signal {tilde over(x)}(n) and processes the DPD input signal using the DPD processingunits 710-730, which operate in parallel. The DPD processing block 700generates the pre-inversed DPD output signal {tilde over (y)}(n), whichis transmitted to a switched mode PA (such as PA 420 or PA 600), wherethe signal is linearized such as shown in FIG. 4.

Because of the aliasing and nonlinearity of the switched mode PA, theDPD processing block 700 is configured to represent and process basebandsignals in both the carrier frequency Fc and one or more higher-orderharmonic zones, such as harmonic frequencies 2Fc and 3Fc.

In some embodiments, the DPD processing unit 710 is substantiallyidentical to the DPD processing block 500 of FIG. 5. Accordingly, theDPD processing unit 710 is configured to process the basebandrepresentation of the DPD input signal {tilde over (x)}(n) at thecarrier frequency Fc according to Equation (20) above.

The DPD processing units 720 and 730 are configured to process thebaseband representation of the DPD input signal {tilde over (x)}(n) atthe m-th harmonic zone. In particular, the DPD processing unit 720processes the baseband representation of the DPD input signal {tildeover (x)}(n) at the m-th harmonic zone using Equation (35). As inEquation (35), the value of m in the DPD processing unit 720 can be anon-negative integer other than one (i.e., m can be 0, 2, 3, 4, . . . ).When m=1, the DPD processing unit 720 operates like the DPD processingunit 710.

Similarly, the DPD processing unit 730 processes the conjugate of thebaseband representation of the DPD input signal, {tilde over (x)}*(n),using Equation (28). As in Equation (28), the value of m in the DPDprocessing unit 730 can be any non-negative integer (i.e., m can be 0,1, 2, 3, . . . ).

Comparing Equations (28) and (35), it can be seen that the DPDprocessing unit 720 uses the m-th power of {tilde over (x)}(n), whilethe DPD processing unit 730 uses the m-th power of the conjugate {tildeover (x)}*(n). The exponent operations are performed in the DPDprocessing units 720, 730 by the exponent operator 725 and the conjugateexponent operator 735, respectively. That is, the DPD processing unit720 receives the baseband representation of the DPD input signal {tildeover (x)}(n) and performs an exponent operation on {tilde over (x)}(n)to {tilde over (x)}^(m) using the exponent operator 725. Likewise, theDPD processing unit 730 receives the baseband representation of the DPDinput signal {tilde over (x)}(n) and performs an exponent operation onthe conjugate {tilde over (x)}*(n) to {tilde over (x)}*^(m) using theconjugate exponent operator 735.

The outputs of the DPD processing block 710-730 are added together toprovide the DPD output signal {tilde over (y)}(n) of the DPD processingblock 700. The output can then be transmitted to the switched mode PA.

In FIG. 7, each of the DPD processing units 710-730 may represent anyhardware or combination of hardware and software/firmware instructions.The hardware here could include any suitable microprocessors,microcontrollers, discrete circuits, or any other processing or controldevices.

Although FIG. 7 illustrates one example of a DPD processing block 700,various changes may be made to FIG. 7. For example, the functionaldivision shown in FIG. 7 is for illustration only. Various components inFIG. 7 could be combined, further subdivided, or omitted and additionalcomponents could be added according to particular needs. Also, thehandling of higher-order harmonics can involve the use of more DPDprocessing units. For instance, in order to process other harmonic zonesin addition to the m-th harmonic zone, other DPD processing units couldbe included in parallel with the DPD processing units 710-730.

FIGS. 8 and 9 illustrate example test results showing an improvement ofnonlinearity using the DPD system 700 according to this disclosure. InFIG. 8, a plot curve 801 depicts an amplitude response of a nonlinearPA, such as a switched mode PA, plotted over a range of frequencies. Aplot curve 802 depicts an amplitude response of the same nonlinear PAcoupled to the DPD processing block 700. As indicated at referencenumerals 803-804, the ACPR of the PA with the DPD is substantiallyreduced compared to the ACPR of the PA without the DPD.

Likewise, FIG. 9 illustrates results from another test with and withoutthe DPD processing block 700. As seen in FIG. 9, a plot curve 902 showsa significant improvement in ACPR when coupled with the DPD processingblock 700 as compared to a plot curve 901, which includes no DPDprocessing.

Although FIGS. 8 and 9 illustrate examples of test results showing animprovement of nonlinearity using the DPD system 700, the examples shownin FIGS. 8 and 9 are for illustration only. Other implementations anduses of the DPD system 700 could provide different test results.

FIG. 10 illustrates an example method 1000 for digital predistortionaccording to this disclosure. For ease of explanation, the method 1000is described with respect to the PA 600 operating with the DPDprocessing block 700 in FIG. 7.

An input signal is received at a digital predistortion block at step1001. This could include, for example, receiving an input signal havingcomponents at a carrier frequency and at one or more harmonicfrequencies at the DPD processing block 700. A baseband representationof the input signal is predistorted at the carrier frequency at step1003. This could include, for example, a first processing unit 710 inthe digital predistortion block 700 predistorting the basebandrepresentation of the input signal at the carrier frequency Fc using oneor more lookup tables.

The baseband representation of the input signal is predistorted at oneor more harmonic frequencies at step 1005. This could include, forexample, a second processing unit 720 in the digital predistortion block700 predistorting the baseband representation of the input signal at thesecond harmonic frequency 2Fc. This could also include a thirdprocessing unit 730 predistorting the conjugate of the basebandrepresentation of the input signal at the second harmonic frequency 2Fc.

An output signal is generated based on the predistorted basebandrepresentation of the input signal at step 1007. This could include, forexample, generating the output signal from a sum of the predistortedoutput signals from the first, second, and third processing units 710,720, 730. The output signal is transmitted to a power amplifier at step1009.

Although FIG. 10 illustrates one example of a method 1000 for digitalpredistortion, various changes may be made to FIG. 10. For example,while FIG. 10 illustrates a series of steps, various steps in eachfigure could overlap, occur in parallel, occur in a different order, oroccur any number of times. Also, one or more of the steps of the method1000 could be removed, or other steps could be added to the method 1000.

In some embodiments, various functions described above are implementedor supported by a computer program that is formed from computer readableprogram code and that is embodied in a computer readable medium. Thephrase “computer readable program code” includes any type of computercode, including source code, object code, and executable code. Thephrase “computer readable medium” includes any type of medium capable ofbeing accessed by a computer, such as read only memory (ROM), randomaccess memory (RAM), a hard disk drive, a compact disc (CD), a digitalvideo disc (DVD), or any other type of memory. A “non-transitory”computer readable medium excludes wired, wireless, optical, or othercommunication links that transport transitory electrical or othersignals. A non-transitory computer readable medium includes media wheredata can be permanently stored and media where data can be stored andlater overwritten, such as a rewritable optical disc or an erasablememory device.

It may be advantageous to set forth definitions of certain words andphrases used throughout this patent document. The terms “application”and “program” refer to one or more computer programs, softwarecomponents, sets of instructions, procedures, functions, objects,classes, instances, related data, or a portion thereof adapted forimplementation in a suitable computer code (including source code,object code, or executable code). The terms “include” and “comprise,” aswell as derivatives thereof, mean inclusion without limitation. The term“or” is inclusive, meaning and/or. The phrase “associated with,” as wellas derivatives thereof, may mean to include, be included within,interconnect with, contain, be contained within, connect to or with,couple to or with, be communicable with, cooperate with, interleave,juxtapose, be proximate to, be bound to or with, have, have a propertyof, have a relationship to or with, or the like. The phrase “at leastone of,” when used with a list of items, means that differentcombinations of one or more of the listed items may be used, and onlyone item in the list may be needed. For example, “at least one of: A, B,and C” includes any of the following combinations: A, B, C, A and B, Aand C, B and C, and A and B and C.

While this disclosure has described certain embodiments and generallyassociated methods, alterations and permutations of these embodimentsand methods will be apparent to those skilled in the art. Accordingly,the above description of example embodiments does not define orconstrain this disclosure. Other changes, substitutions, and alterationsare also possible without departing from the spirit and scope of thisdisclosure, as defined by the following claims.

What is claimed is:
 1. A method comprising: receiving an input signal;predistorting a baseband representation of the input signal at a carrierfrequency and at one or more harmonic frequencies; generating an outputsignal based on the predistorted baseband representation of the inputsignal; and transmitting the output signal to a power amplifier; whereinpredistorting the baseband representation of the input signal at the oneor more harmonic frequencies comprises predistorting based on an m-thpower of the baseband representation of the input signal andpredistorting based on an m-th power of a conjugate of the basebandrepresentation of the input signal, wherein m is a positive integer. 2.An apparatus comprising: a digital predistortion block comprising: afirst processing unit configured to receive an input signal andpredistort a baseband representation of the input signal at a carrierfrequency; and second processing units configured to receive the inputsignal and predistort a baseband representation of the input signal atone or more harmonic frequencies; the digital predistortion blockconfigured to generate an output signal based on the predistortedbaseband representation of the input signal and transmit the outputsignal to a power amplifier; wherein the second processing units areconfigured to predistort based on an m-th power of the basebandrepresentation of the input signal and predistort based on an m-th powerof a conjugate of the baseband representation of the input signal,wherein m is a positive integer.
 3. A non-transitory computer readablemedium encoded with computer-executable instructions that when executedcause at least one processing device to: receive an input signal;predistort a baseband representation of the input signal at a carrierfrequency and at one or more harmonic frequencies; generate an outputsignal based on the predistorted baseband representation of the inputsignal; and transmit the output signal to a power amplifier; wherein theinstructions that when executed cause the at least one processing deviceto predistort the baseband representation of the input signal at the oneor more harmonic frequencies comprise: instructions that when executedcause the at least one processing device to predistort based on an m-thpower of the baseband representation of the input signal andpredistorting based on an m-th power of a conjugate of the basebandrepresentation of the input signal, wherein m is a positive integer.